Depending on what the client’s goals are, frequent assessments may be necessary. This is to help adjust the program to continue to suit their goals. Although you may have a full program written at the start of their training (with progressions all set in place and the numbers taken care of), you can’t really expect your client to necessarily fit your program design every step of the way. It’s more important that the program design fits your client every step of the way instead.
Now, depending on your program design, you may have it so that every exercise is an assessment for your next workout session. You don’t necessarily need to do formal testing to measure all areas of fitness. Again, the client’s goals will dictate your priorities for what to assess and how often you will assess.
What you charge for assessments is up to your business model. I would say let assessments be free if they are informal or if they are already a part of the workout routine (such as checking proper form with each exercise if one of the client’s goals is related to corrective exercise). Regardless, assessments (whether free or not) are never a waste of your time, unless you don’t use the information to write your program. There has to be a point as to why you are assessing.